Parallel Adaptive Lagrangian Discontinuous Galerkin Simulation of Pediatric Brain Injury

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The overall goal of this work is to develop the computational tools to better study "shaken baby syndrome". This project will develop highly accurate parallel adaptive Lagrangian discontinuous Galerkin techniques for the simulation of fluid mechanics and solid mechanics. These techniques will be central to the development of high fidelity simulation tools for investigation of pediatric brain injury mechanisms and preventative strategies. Even the most powerful computers today using the best available codes would need weeks or months to do these calculations. Moreover, even those heroic calculations would not provide reasonable simulations due to the poor numerical accuracy of the lower order (O(h)) finite element / finite difference schemes and explicit time integration schemes (O(Dt)) used.The key element of the new strategy is the development and use of parallel adaptive hp Lagrangian discontinuous Galerkin schemes that provide the accuracy and efficiency necessary for dealing with the complex geometric and material structure of the brain tissue, associated membranes, and blood vessels. These schemes will enable the use of higher order approximations to obtain accuracies that are O(hp) and O(Dtk), for p, k 1. While the pediatric brain injury application will drive the research into this new class of parallel computational techniques, the codes and methodology should be useful for a much wider class of problems.